Compressive sensing is a novel sampling/sensing paradigm that enables significant reduction in sampling and computation costs for signals with sparse or compressible representation. This technique has experienced rapid growth in recent years and has attracted attention in electrical engineering, optics, signal processing, statistics and computer science. Using compressive sensing techniques, the number of measurements needed to construct an image of a scanned object is greatly reduced compared to traditional methods, particularly when the signal is sparse in a known basis. The fundamental idea behind compressive sensing is, rather than first sampling at a high rate followed by compressing the sampled data, an improvement in data recovery is obtained when the data is directly sampled. Compression is achieved with direct sampling, resulting in an output data in a compressed format. For example, efficient sampling protocols may be designed to capture small amounts of useful signal information in a sparse domain. After sampling, the full-length signal is reconstructed using numerical optimization algorithms.
Compressive sensing techniques have been applied to microwave imaging systems employing a guided wave metamaterial aperture to generate different radiation patterns for compressive sensing. The reconstruction of compressive images at 10 frames per second was achieved at K-band. However, the radiation patterns generated by the metamaterial aperture were random and the sampling protocol was not optimized to capture the signal information. In the present invention, a plurality of optimization algorithms are used to create a plurality of optimized projections. An optimized radiation pattern based on the plurality of optimized projections, as opposed to a random radiation pattern, can then be realized. One such optimization algorithm is the Principal Component Analysis (“PCA”) as detailed in “Reconfigurable Array Design to Realize Principal Component Analysis (PCA) Based Microwave Compressive Sensing Imaging System”, Xin et al, which is incorporated herein in its entirety.
PCA is one of the most commonly used tools in statistics and data-mining areas for compression and classification of data. The purpose of PCA is to reduce the dimensionality of a data set having a large number of interrelated variables by transforming it to a new set having a smaller number of variables, while retaining as much of the sample information as possible [3]. These new variables, called principal components (“PCs”), are uncorrelated and ordered by the fraction of the total information each retains. Therefore, keeping only the values of the first few principal components would still retain most of the information from all the original variables. In practice, this PCA is achieved by calculating the covariance matrix of the full data set. The eigenvectors and eigenvalues of the covariance matrix are then computed and sorted according to decreasing eigenvalues. Compared to a random-pattern-based compressive sensing system, fewer numbers of measurements are required for optimized-radiation-pattern-based compressive sensing systems (such as the PCA based system) to achieve the same performance.
A direct application of the present invention would be security screening systems at places such as airports, train stations, or museums. The current security screening processes often encompass long lines, complex rules, and invasive methods. Further, the current security screening systems are inefficient, bulky, and costly. A faster, more accurate and cost-efficient security screening system is necessary and can be realized by the present invention.
Any feature or combination of features described herein are included within the scope of the present invention provided that the features included in any such combination are not mutually inconsistent as will be apparent from the context, this specification, and the knowledge of one of ordinary skill in the art. Additional advantages and aspects of the present invention are apparent in the following detailed description and claims.